Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [425,2,Mod(49,425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(425, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("425.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 425 = 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 425.n (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.39364208590\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 85) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 399.4 | ||
Character | \(\chi\) | \(=\) | 425.399 |
Dual form | 425.2.n.c.49.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/425\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.254738 | + | 0.254738i | 0.180127 | + | 0.180127i | 0.791411 | − | 0.611284i | \(-0.209347\pi\) |
−0.611284 | + | 0.791411i | \(0.709347\pi\) | |||||||
\(3\) | 0.0501087 | + | 0.0207557i | 0.0289303 | + | 0.0119833i | 0.397102 | − | 0.917775i | \(-0.370016\pi\) |
−0.368171 | + | 0.929758i | \(0.620016\pi\) | |||||||
\(4\) | − | 1.87022i | − | 0.935108i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.00747733 | + | 0.0180519i | 0.00305261 | + | 0.00736965i | ||||
\(7\) | −0.114315 | − | 0.275980i | −0.0432068 | − | 0.104310i | 0.900803 | − | 0.434228i | \(-0.142979\pi\) |
−0.944010 | + | 0.329918i | \(0.892979\pi\) | |||||||
\(8\) | 0.985893 | − | 0.985893i | 0.348566 | − | 0.348566i | ||||
\(9\) | −2.11924 | − | 2.11924i | −0.706413 | − | 0.706413i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.05900 | − | 2.55665i | −0.319301 | − | 0.770860i | −0.999291 | − | 0.0376394i | \(-0.988016\pi\) |
0.679991 | − | 0.733221i | \(-0.261984\pi\) | |||||||
\(12\) | 0.0388177 | − | 0.0937141i | 0.0112057 | − | 0.0270529i | ||||
\(13\) | 1.97956 | 0.549030 | 0.274515 | − | 0.961583i | \(-0.411483\pi\) | ||||
0.274515 | + | 0.961583i | \(0.411483\pi\) | |||||||
\(14\) | 0.0411823 | − | 0.0994229i | 0.0110064 | − | 0.0265719i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.23814 | −0.809536 | ||||||||
\(17\) | −3.94094 | + | 1.21202i | −0.955818 | + | 0.293959i | ||||
\(18\) | − | 1.07970i | − | 0.254489i | ||||||
\(19\) | 1.99331 | − | 1.99331i | 0.457296 | − | 0.457296i | −0.440471 | − | 0.897767i | \(-0.645188\pi\) |
0.897767 | + | 0.440471i | \(0.145188\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.0162017i | − | 0.00353549i | ||||||
\(22\) | 0.381510 | − | 0.921046i | 0.0813382 | − | 0.196368i | ||||
\(23\) | 6.22672 | − | 2.57919i | 1.29836 | − | 0.537799i | 0.376895 | − | 0.926256i | \(-0.376992\pi\) |
0.921467 | + | 0.388457i | \(0.126992\pi\) | |||||||
\(24\) | 0.0698647 | − | 0.0289389i | 0.0142611 | − | 0.00590713i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.504269 | + | 0.504269i | 0.0988953 | + | 0.0988953i | ||||
\(27\) | −0.124473 | − | 0.300505i | −0.0239549 | − | 0.0578322i | ||||
\(28\) | −0.516142 | + | 0.213793i | −0.0975416 | + | 0.0404031i | ||||
\(29\) | −4.36632 | − | 1.80859i | −0.810806 | − | 0.335847i | −0.0615305 | − | 0.998105i | \(-0.519598\pi\) |
−0.749276 | + | 0.662258i | \(0.769598\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.15808 | − | 2.79584i | 0.207997 | − | 0.502148i | −0.785111 | − | 0.619355i | \(-0.787394\pi\) |
0.993108 | + | 0.117207i | \(0.0373941\pi\) | |||||||
\(32\) | −2.79667 | − | 2.79667i | −0.494385 | − | 0.494385i | ||||
\(33\) | − | 0.150091i | − | 0.0261275i | ||||||
\(34\) | −1.31266 | − | 0.695159i | −0.225119 | − | 0.119219i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.96344 | + | 3.96344i | −0.660573 | + | 0.660573i | ||||
\(37\) | 8.70414 | + | 3.60537i | 1.43095 | + | 0.592719i | 0.957586 | − | 0.288147i | \(-0.0930392\pi\) |
0.473365 | + | 0.880866i | \(0.343039\pi\) | |||||||
\(38\) | 1.01554 | 0.164743 | ||||||||
\(39\) | 0.0991930 | + | 0.0410871i | 0.0158836 | + | 0.00657920i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.87301 | − | 1.19004i | 0.448688 | − | 0.185853i | −0.146885 | − | 0.989154i | \(-0.546925\pi\) |
0.595574 | + | 0.803301i | \(0.296925\pi\) | |||||||
\(42\) | 0.00412718 | − | 0.00412718i | 0.000636838 | − | 0.000636838i | ||||
\(43\) | −5.78771 | + | 5.78771i | −0.882617 | + | 0.882617i | −0.993800 | − | 0.111183i | \(-0.964536\pi\) |
0.111183 | + | 0.993800i | \(0.464536\pi\) | |||||||
\(44\) | −4.78150 | + | 1.98056i | −0.720838 | + | 0.298581i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.24320 | + | 0.929166i | 0.330742 | + | 0.136998i | ||||
\(47\) | 1.08341 | 0.158032 | 0.0790159 | − | 0.996873i | \(-0.474822\pi\) | ||||
0.0790159 | + | 0.996873i | \(0.474822\pi\) | |||||||
\(48\) | −0.162259 | − | 0.0672100i | −0.0234201 | − | 0.00970092i | ||||
\(49\) | 4.88665 | − | 4.88665i | 0.698093 | − | 0.698093i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.222632 | − | 0.0210640i | −0.0311747 | − | 0.00294954i | ||||
\(52\) | − | 3.70220i | − | 0.513403i | ||||||
\(53\) | −1.89858 | − | 1.89858i | −0.260790 | − | 0.260790i | 0.564585 | − | 0.825375i | \(-0.309036\pi\) |
−0.825375 | + | 0.564585i | \(0.809036\pi\) | |||||||
\(54\) | 0.0448420 | − | 0.108258i | 0.00610222 | − | 0.0147321i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.384788 | − | 0.159384i | −0.0514195 | − | 0.0212986i | ||||
\(57\) | 0.141255 | − | 0.0585096i | 0.0187096 | − | 0.00774979i | ||||
\(58\) | −0.651553 | − | 1.57299i | −0.0855531 | − | 0.206543i | ||||
\(59\) | 6.47310 | + | 6.47310i | 0.842726 | + | 0.842726i | 0.989213 | − | 0.146487i | \(-0.0467966\pi\) |
−0.146487 | + | 0.989213i | \(0.546797\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3418 | − | 4.28372i | 1.32413 | − | 0.548474i | 0.395158 | − | 0.918613i | \(-0.370690\pi\) |
0.928976 | + | 0.370139i | \(0.120690\pi\) | |||||||
\(62\) | 1.00722 | − | 0.417202i | 0.127916 | − | 0.0529847i | ||||
\(63\) | −0.342607 | + | 0.827127i | −0.0431645 | + | 0.104208i | ||||
\(64\) | 5.05145i | 0.631432i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.0382339 | − | 0.0382339i | 0.00470627 | − | 0.00470627i | ||||
\(67\) | 12.5585i | 1.53427i | 0.641488 | + | 0.767133i | \(0.278317\pi\) | ||||
−0.641488 | + | 0.767133i | \(0.721683\pi\) | |||||||
\(68\) | 2.26675 | + | 7.37041i | 0.274884 | + | 0.893793i | ||||
\(69\) | 0.365546 | 0.0440066 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.25315 | + | 5.43960i | −0.267400 | + | 0.645561i | −0.999359 | − | 0.0357872i | \(-0.988606\pi\) |
0.731959 | + | 0.681348i | \(0.238606\pi\) | |||||||
\(72\) | −4.17869 | −0.492463 | ||||||||
\(73\) | 0.0829144 | − | 0.200173i | 0.00970440 | − | 0.0234285i | −0.918953 | − | 0.394367i | \(-0.870964\pi\) |
0.928657 | + | 0.370938i | \(0.120964\pi\) | |||||||
\(74\) | 1.29885 | + | 3.13570i | 0.150988 | + | 0.364518i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.72792 | − | 3.72792i | −0.427622 | − | 0.427622i | ||||
\(77\) | −0.584525 | + | 0.584525i | −0.0666128 | + | 0.0666128i | ||||
\(78\) | 0.0148018 | + | 0.0357347i | 0.00167598 | + | 0.00404616i | ||||
\(79\) | 4.07771 | + | 9.84447i | 0.458779 | + | 1.10759i | 0.968892 | + | 0.247482i | \(0.0796032\pi\) |
−0.510114 | + | 0.860107i | \(0.670397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.97353i | 0.997059i | ||||||||
\(82\) | 1.03501 | + | 0.428717i | 0.114298 | + | 0.0473438i | ||||
\(83\) | −11.0129 | − | 11.0129i | −1.20883 | − | 1.20883i | −0.971407 | − | 0.237421i | \(-0.923698\pi\) |
−0.237421 | − | 0.971407i | \(-0.576302\pi\) | |||||||
\(84\) | −0.0303006 | −0.00330607 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.94870 | −0.317967 | ||||||||
\(87\) | −0.181252 | − | 0.181252i | −0.0194323 | − | 0.0194323i | ||||
\(88\) | −3.56465 | − | 1.47653i | −0.379993 | − | 0.157398i | ||||
\(89\) | 1.55264i | 0.164579i | 0.996608 | + | 0.0822897i | \(0.0262233\pi\) | ||||
−0.996608 | + | 0.0822897i | \(0.973777\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.226292 | − | 0.546318i | −0.0237219 | − | 0.0572696i | ||||
\(92\) | −4.82365 | − | 11.6453i | −0.502900 | − | 1.21411i | ||||
\(93\) | 0.116059 | − | 0.116059i | 0.0120348 | − | 0.0120348i | ||||
\(94\) | 0.275986 | + | 0.275986i | 0.0284658 | + | 0.0284658i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.0820905 | − | 0.198184i | −0.00837833 | − | 0.0202271i | ||||
\(97\) | 3.43280 | − | 8.28752i | 0.348549 | − | 0.841471i | −0.648243 | − | 0.761433i | \(-0.724496\pi\) |
0.996792 | − | 0.0800373i | \(-0.0255040\pi\) | |||||||
\(98\) | 2.48963 | 0.251491 | ||||||||
\(99\) | −3.17389 | + | 7.66244i | −0.318988 | + | 0.770104i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.92132 | −0.688697 | −0.344349 | − | 0.938842i | \(-0.611900\pi\) | ||||
−0.344349 | + | 0.938842i | \(0.611900\pi\) | |||||||
\(102\) | −0.0513470 | − | 0.0620786i | −0.00508412 | − | 0.00614670i | ||||
\(103\) | 12.9642i | 1.27740i | 0.769457 | + | 0.638699i | \(0.220527\pi\) | ||||
−0.769457 | + | 0.638699i | \(0.779473\pi\) | |||||||
\(104\) | 1.95163 | − | 1.95163i | 0.191373 | − | 0.191373i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 0.967283i | − | 0.0939508i | ||||||
\(107\) | −1.38670 | + | 3.34779i | −0.134058 | + | 0.323643i | −0.976626 | − | 0.214946i | \(-0.931043\pi\) |
0.842568 | + | 0.538589i | \(0.181043\pi\) | |||||||
\(108\) | −0.562009 | + | 0.232792i | −0.0540793 | + | 0.0224004i | ||||
\(109\) | 4.75832 | − | 1.97096i | 0.455764 | − | 0.188784i | −0.142977 | − | 0.989726i | \(-0.545668\pi\) |
0.598742 | + | 0.800942i | \(0.295668\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.361321 | + | 0.361321i | 0.0342951 | + | 0.0342951i | ||||
\(112\) | 0.370167 | + | 0.893662i | 0.0349775 | + | 0.0844431i | ||||
\(113\) | −10.1687 | + | 4.21202i | −0.956593 | + | 0.396234i | −0.805705 | − | 0.592317i | \(-0.798213\pi\) |
−0.150888 | + | 0.988551i | \(0.548213\pi\) | |||||||
\(114\) | 0.0508876 | + | 0.0210783i | 0.00476606 | + | 0.00197417i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.38246 | + | 8.16597i | −0.314053 | + | 0.758192i | ||||
\(117\) | −4.19516 | − | 4.19516i | −0.387842 | − | 0.387842i | ||||
\(118\) | 3.29789i | 0.303596i | ||||||||
\(119\) | 0.785001 | + | 0.949067i | 0.0719609 | + | 0.0870008i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.36318 | − | 2.36318i | 0.214834 | − | 0.214834i | ||||
\(122\) | 3.72569 | + | 1.54323i | 0.337308 | + | 0.139717i | ||||
\(123\) | 0.168663 | 0.0152078 | ||||||||
\(124\) | −5.22883 | − | 2.16585i | −0.469563 | − | 0.194499i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.297976 | + | 0.123426i | −0.0265458 | + | 0.0109956i | ||||
\(127\) | 5.18472 | − | 5.18472i | 0.460070 | − | 0.460070i | −0.438608 | − | 0.898678i | \(-0.644528\pi\) |
0.898678 | + | 0.438608i | \(0.144528\pi\) | |||||||
\(128\) | −6.88013 | + | 6.88013i | −0.608123 | + | 0.608123i | ||||
\(129\) | −0.410143 | + | 0.169887i | −0.0361110 | + | 0.0149577i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.0035 | + | 6.62885i | 1.39823 | + | 0.579166i | 0.949291 | − | 0.314397i | \(-0.101802\pi\) |
0.448938 | + | 0.893563i | \(0.351802\pi\) | |||||||
\(132\) | −0.280703 | −0.0244320 | ||||||||
\(133\) | −0.777977 | − | 0.322249i | −0.0674592 | − | 0.0279425i | ||||
\(134\) | −3.19913 | + | 3.19913i | −0.276363 | + | 0.276363i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.69042 | + | 5.08027i | −0.230701 | + | 0.435629i | ||||
\(137\) | 13.9745i | 1.19392i | 0.802272 | + | 0.596959i | \(0.203625\pi\) | ||||
−0.802272 | + | 0.596959i | \(0.796375\pi\) | |||||||
\(138\) | 0.0931186 | + | 0.0931186i | 0.00792678 | + | 0.00792678i | ||||
\(139\) | 1.38555 | − | 3.34501i | 0.117521 | − | 0.283720i | −0.854163 | − | 0.520005i | \(-0.825930\pi\) |
0.971684 | + | 0.236285i | \(0.0759300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0542883 | + | 0.0224870i | 0.00457190 | + | 0.00189374i | ||||
\(142\) | −1.95964 | + | 0.811709i | −0.164449 | + | 0.0681171i | ||||
\(143\) | −2.09635 | − | 5.06104i | −0.175306 | − | 0.423226i | ||||
\(144\) | 6.86241 | + | 6.86241i | 0.571867 | + | 0.571867i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.0721133 | − | 0.0298703i | 0.00596814 | − | 0.00247208i | ||||
\(147\) | 0.346290 | − | 0.143438i | 0.0285615 | − | 0.0118306i | ||||
\(148\) | 6.74283 | − | 16.2786i | 0.554257 | − | 1.33809i | ||||
\(149\) | − | 12.8580i | − | 1.05336i | −0.850062 | − | 0.526682i | \(-0.823436\pi\) | ||
0.850062 | − | 0.526682i | \(-0.176564\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.5511 | − | 13.5511i | 1.10277 | − | 1.10277i | 0.108700 | − | 0.994075i | \(-0.465331\pi\) |
0.994075 | − | 0.108700i | \(-0.0346687\pi\) | |||||||
\(152\) | − | 3.93038i | − | 0.318796i | ||||||
\(153\) | 10.9204 | + | 5.78322i | 0.882859 | + | 0.467546i | ||||
\(154\) | −0.297802 | −0.0239976 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.0768418 | − | 0.185512i | 0.00615227 | − | 0.0148529i | ||||
\(157\) | 2.70222 | 0.215661 | 0.107830 | − | 0.994169i | \(-0.465610\pi\) | ||||
0.107830 | + | 0.994169i | \(0.465610\pi\) | |||||||
\(158\) | −1.46901 | + | 3.54651i | −0.116868 | + | 0.282146i | ||||
\(159\) | −0.0557290 | − | 0.134542i | −0.00441960 | − | 0.0106699i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.42361 | − | 1.42361i | −0.112196 | − | 0.112196i | ||||
\(162\) | −2.28590 | + | 2.28590i | −0.179598 | + | 0.179598i | ||||
\(163\) | −6.54609 | − | 15.8036i | −0.512729 | − | 1.23784i | −0.942290 | − | 0.334799i | \(-0.891332\pi\) |
0.429561 | − | 0.903038i | \(-0.358668\pi\) | |||||||
\(164\) | −2.22563 | − | 5.37315i | −0.173792 | − | 0.419572i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 5.61084i | − | 0.435486i | ||||||
\(167\) | −8.17871 | − | 3.38773i | −0.632887 | − | 0.262151i | 0.0430919 | − | 0.999071i | \(-0.486279\pi\) |
−0.675979 | + | 0.736921i | \(0.736279\pi\) | |||||||
\(168\) | −0.0159731 | − | 0.0159731i | −0.00123235 | − | 0.00123235i | ||||
\(169\) | −9.08135 | −0.698566 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.44860 | −0.646081 | ||||||||
\(172\) | 10.8243 | + | 10.8243i | 0.825343 | + | 0.825343i | ||||
\(173\) | 17.7246 | + | 7.34175i | 1.34757 | + | 0.558183i | 0.935616 | − | 0.353020i | \(-0.114845\pi\) |
0.411957 | + | 0.911203i | \(0.364845\pi\) | |||||||
\(174\) | − | 0.0923438i | − | 0.00700057i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.42920 | + | 8.27881i | 0.258485 | + | 0.624039i | ||||
\(177\) | 0.190005 | + | 0.458712i | 0.0142816 | + | 0.0344789i | ||||
\(178\) | −0.395517 | + | 0.395517i | −0.0296452 | + | 0.0296452i | ||||
\(179\) | 3.06554 | + | 3.06554i | 0.229129 | + | 0.229129i | 0.812329 | − | 0.583200i | \(-0.198199\pi\) |
−0.583200 | + | 0.812329i | \(0.698199\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.09958 | − | 21.9683i | −0.676366 | − | 1.63289i | −0.770582 | − | 0.637341i | \(-0.780034\pi\) |
0.0942155 | − | 0.995552i | \(-0.469966\pi\) | |||||||
\(182\) | 0.0815228 | − | 0.196813i | 0.00604287 | − | 0.0145888i | ||||
\(183\) | 0.607127 | 0.0448801 | ||||||||
\(184\) | 3.59607 | − | 8.68169i | 0.265106 | − | 0.640022i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.0591296 | 0.00433559 | ||||||||
\(187\) | 7.27219 | + | 8.79208i | 0.531795 | + | 0.642941i | ||||
\(188\) | − | 2.02621i | − | 0.147777i | ||||||
\(189\) | −0.0687041 | + | 0.0687041i | −0.00499749 | + | 0.00499749i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.27055i | 0.526079i | 0.964785 | + | 0.263039i | \(0.0847249\pi\) | ||||
−0.964785 | + | 0.263039i | \(0.915275\pi\) | |||||||
\(192\) | −0.104846 | + | 0.253122i | −0.00756664 | + | 0.0182675i | ||||
\(193\) | 20.5094 | − | 8.49528i | 1.47630 | − | 0.611504i | 0.508015 | − | 0.861348i | \(-0.330380\pi\) |
0.968286 | + | 0.249845i | \(0.0803795\pi\) | |||||||
\(194\) | 2.98562 | − | 1.23668i | 0.214355 | − | 0.0887887i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.13910 | − | 9.13910i | −0.652793 | − | 0.652793i | ||||
\(197\) | −1.71496 | − | 4.14027i | −0.122186 | − | 0.294982i | 0.850938 | − | 0.525267i | \(-0.176034\pi\) |
−0.973123 | + | 0.230284i | \(0.926034\pi\) | |||||||
\(198\) | −2.76043 | + | 1.14341i | −0.196175 | + | 0.0812584i | ||||
\(199\) | 0.368987 | + | 0.152839i | 0.0261568 | + | 0.0108345i | 0.395723 | − | 0.918370i | \(-0.370494\pi\) |
−0.369567 | + | 0.929204i | \(0.620494\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.260661 | + | 0.629290i | −0.0183856 | + | 0.0443867i | ||||
\(202\) | −1.76313 | − | 1.76313i | −0.124053 | − | 0.124053i | ||||
\(203\) | 1.41176i | 0.0990865i | ||||||||
\(204\) | −0.0393942 | + | 0.416370i | −0.00275814 | + | 0.0291517i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.30247 | + | 3.30247i | −0.230094 | + | 0.230094i | ||||
\(207\) | −18.6618 | − | 7.72999i | −1.29709 | − | 0.537271i | ||||
\(208\) | −6.41009 | −0.444460 | ||||||||
\(209\) | −7.20712 | − | 2.98529i | −0.498527 | − | 0.206497i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.80171 | + | 0.746294i | −0.124035 | + | 0.0513770i | −0.443838 | − | 0.896107i | \(-0.646383\pi\) |
0.319803 | + | 0.947484i | \(0.396383\pi\) | |||||||
\(212\) | −3.55076 | + | 3.55076i | −0.243867 | + | 0.243867i | ||||
\(213\) | −0.225805 | + | 0.225805i | −0.0154719 | + | 0.0154719i | ||||
\(214\) | −1.20606 | + | 0.499566i | −0.0824444 | + | 0.0341496i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.418983 | − | 0.173548i | −0.0285082 | − | 0.0118085i | ||||
\(217\) | −0.903981 | −0.0613662 | ||||||||
\(218\) | 1.71421 | + | 0.710047i | 0.116101 | + | 0.0480905i | ||||
\(219\) | 0.00830947 | − | 0.00830947i | 0.000561502 | − | 0.000561502i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.80131 | + | 2.39927i | −0.524773 | + | 0.161393i | ||||
\(222\) | 0.184085i | 0.0123550i | ||||||||
\(223\) | 16.7800 | + | 16.7800i | 1.12367 | + | 1.12367i | 0.991184 | + | 0.132491i | \(0.0422974\pi\) |
0.132491 | + | 0.991184i | \(0.457703\pi\) | |||||||
\(224\) | −0.452123 | + | 1.09152i | −0.0302088 | + | 0.0729304i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.66333 | − | 1.51740i | −0.243681 | − | 0.100936i | ||||
\(227\) | 18.9948 | − | 7.86790i | 1.26073 | − | 0.522211i | 0.350595 | − | 0.936527i | \(-0.385979\pi\) |
0.910133 | + | 0.414316i | \(0.135979\pi\) | |||||||
\(228\) | −0.109426 | − | 0.264177i | −0.00724689 | − | 0.0174955i | ||||
\(229\) | −18.8066 | − | 18.8066i | −1.24277 | − | 1.24277i | −0.958846 | − | 0.283928i | \(-0.908362\pi\) |
−0.283928 | − | 0.958846i | \(-0.591638\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.0414220 | + | 0.0171576i | −0.00272537 | + | 0.00112889i | ||||
\(232\) | −6.08780 | + | 2.52165i | −0.399684 | + | 0.165554i | ||||
\(233\) | 8.99275 | − | 21.7104i | 0.589135 | − | 1.42230i | −0.295196 | − | 0.955437i | \(-0.595385\pi\) |
0.884331 | − | 0.466860i | \(-0.154615\pi\) | |||||||
\(234\) | − | 2.13734i | − | 0.139722i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.1061 | − | 12.1061i | 0.788040 | − | 0.788040i | ||||
\(237\) | 0.577929i | 0.0375405i | ||||||||
\(238\) | −0.0417939 | + | 0.441734i | −0.00270910 | + | 0.0286333i | ||||
\(239\) | −5.25737 | −0.340071 | −0.170036 | − | 0.985438i | \(-0.554388\pi\) | ||||
−0.170036 | + | 0.985438i | \(0.554388\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.08146 | − | 5.02509i | 0.134079 | − | 0.323694i | −0.842553 | − | 0.538613i | \(-0.818949\pi\) |
0.976632 | + | 0.214918i | \(0.0689486\pi\) | |||||||
\(242\) | 1.20398 | 0.0773950 | ||||||||
\(243\) | −0.559671 | + | 1.35117i | −0.0359029 | + | 0.0866774i | ||||
\(244\) | −8.01149 | − | 19.3414i | −0.512883 | − | 1.23821i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0429649 | + | 0.0429649i | 0.00273934 | + | 0.00273934i | ||||
\(247\) | 3.94587 | − | 3.94587i | 0.251070 | − | 0.251070i | ||||
\(248\) | −1.61466 | − | 3.89814i | −0.102531 | − | 0.247532i | ||||
\(249\) | −0.323263 | − | 0.780426i | −0.0204860 | − | 0.0494575i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.3864i | 1.66550i | 0.553652 | + | 0.832748i | \(0.313234\pi\) | ||||
−0.553652 | + | 0.832748i | \(0.686766\pi\) | |||||||
\(252\) | 1.54691 | + | 0.640750i | 0.0974460 | + | 0.0403634i | ||||
\(253\) | −13.1882 | − | 13.1882i | −0.829135 | − | 0.829135i | ||||
\(254\) | 2.64150 | 0.165742 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.59764 | 0.412352 | ||||||||
\(257\) | −13.2589 | − | 13.2589i | −0.827065 | − | 0.827065i | 0.160045 | − | 0.987110i | \(-0.448836\pi\) |
−0.987110 | + | 0.160045i | \(0.948836\pi\) | |||||||
\(258\) | −0.147756 | − | 0.0612024i | −0.00919887 | − | 0.00381030i | ||||
\(259\) | − | 2.81431i | − | 0.174873i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.42045 | + | 13.0861i | 0.335518 | + | 0.810011i | ||||
\(262\) | 2.38807 | + | 5.76532i | 0.147536 | + | 0.356183i | ||||
\(263\) | −11.3145 | + | 11.3145i | −0.697680 | + | 0.697680i | −0.963910 | − | 0.266230i | \(-0.914222\pi\) |
0.266230 | + | 0.963910i | \(0.414222\pi\) | |||||||
\(264\) | −0.147974 | − | 0.147974i | −0.00910714 | − | 0.00910714i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.116091 | − | 0.280270i | −0.00711803 | − | 0.0171844i | ||||
\(267\) | −0.0322261 | + | 0.0778007i | −0.00197221 | + | 0.00476133i | ||||
\(268\) | 23.4871 | 1.43470 | ||||||||
\(269\) | −0.457836 | + | 1.10531i | −0.0279147 | + | 0.0673922i | −0.937222 | − | 0.348733i | \(-0.886612\pi\) |
0.909307 | + | 0.416125i | \(0.136612\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.888590 | −0.0539780 | −0.0269890 | − | 0.999636i | \(-0.508592\pi\) | ||||
−0.0269890 | + | 0.999636i | \(0.508592\pi\) | |||||||
\(272\) | 12.7613 | − | 3.92471i | 0.773769 | − | 0.237971i | ||||
\(273\) | − | 0.0320721i | − | 0.00194109i | ||||||
\(274\) | −3.55983 | + | 3.55983i | −0.215057 | + | 0.215057i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 0.683650i | − | 0.0411509i | ||||||
\(277\) | −2.36450 | + | 5.70841i | −0.142069 | + | 0.342985i | −0.978858 | − | 0.204540i | \(-0.934430\pi\) |
0.836789 | + | 0.547525i | \(0.184430\pi\) | |||||||
\(278\) | 1.20505 | − | 0.499150i | 0.0722744 | − | 0.0299370i | ||||
\(279\) | −8.37931 | + | 3.47082i | −0.501656 | + | 0.207793i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.7250 | − | 19.7250i | −1.17670 | − | 1.17670i | −0.980581 | − | 0.196117i | \(-0.937167\pi\) |
−0.196117 | − | 0.980581i | \(-0.562833\pi\) | |||||||
\(282\) | 0.00810103 | + | 0.0195576i | 0.000482409 | + | 0.00116464i | ||||
\(283\) | −27.4503 | + | 11.3703i | −1.63175 | + | 0.675893i | −0.995427 | − | 0.0955282i | \(-0.969546\pi\) |
−0.636324 | + | 0.771422i | \(0.719546\pi\) | |||||||
\(284\) | 10.1732 | + | 4.21389i | 0.603670 | + | 0.250048i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.755221 | − | 1.82326i | 0.0446571 | − | 0.107812i | ||||
\(287\) | −0.656853 | − | 0.656853i | −0.0387728 | − | 0.0387728i | ||||
\(288\) | 11.8536i | 0.698481i | ||||||||
\(289\) | 14.0620 | − | 9.55303i | 0.827176 | − | 0.561943i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.344027 | − | 0.344027i | 0.0201672 | − | 0.0201672i | ||||
\(292\) | −0.374367 | − | 0.155068i | −0.0219082 | − | 0.00907466i | ||||
\(293\) | 22.4626 | 1.31228 | 0.656140 | − | 0.754639i | \(-0.272188\pi\) | ||||
0.656140 | + | 0.754639i | \(0.272188\pi\) | |||||||
\(294\) | 0.124752 | + | 0.0516741i | 0.00727571 | + | 0.00301370i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.1359 | − | 5.02684i | 0.705382 | − | 0.292179i | ||||
\(297\) | −0.636470 | + | 0.636470i | −0.0369317 | + | 0.0369317i | ||||
\(298\) | 3.27542 | − | 3.27542i | 0.189740 | − | 0.189740i | ||||
\(299\) | 12.3262 | − | 5.10566i | 0.712840 | − | 0.295268i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.25891 | + | 0.935671i | 0.130201 | + | 0.0539312i | ||||
\(302\) | 6.90398 | 0.397279 | ||||||||
\(303\) | −0.346818 | − | 0.143657i | −0.0199242 | − | 0.00825287i | ||||
\(304\) | −6.45462 | + | 6.45462i | −0.370198 | + | 0.370198i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.30863 | + | 4.25505i | 0.0748093 | + | 0.243245i | ||||
\(307\) | − | 5.53854i | − | 0.316101i | −0.987431 | − | 0.158050i | \(-0.949479\pi\) | ||
0.987431 | − | 0.158050i | \(-0.0505209\pi\) | |||||||
\(308\) | 1.09319 | + | 1.09319i | 0.0622902 | + | 0.0622902i | ||||
\(309\) | −0.269080 | + | 0.649618i | −0.0153075 | + | 0.0369555i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.8510 | − | 8.63675i | −1.18235 | − | 0.489745i | −0.297093 | − | 0.954849i | \(-0.596017\pi\) |
−0.885256 | + | 0.465104i | \(0.846017\pi\) | |||||||
\(312\) | 0.138301 | − | 0.0572862i | 0.00782976 | − | 0.00324319i | ||||
\(313\) | −4.66325 | − | 11.2581i | −0.263583 | − | 0.636345i | 0.735572 | − | 0.677446i | \(-0.236913\pi\) |
−0.999155 | + | 0.0411013i | \(0.986913\pi\) | |||||||
\(314\) | 0.688359 | + | 0.688359i | 0.0388463 | + | 0.0388463i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18.4113 | − | 7.62621i | 1.03572 | − | 0.429008i | ||||
\(317\) | −20.3043 | + | 8.41030i | −1.14040 | + | 0.472370i | −0.871304 | − | 0.490743i | \(-0.836725\pi\) |
−0.269097 | + | 0.963113i | \(0.586725\pi\) | |||||||
\(318\) | 0.0200766 | − | 0.0484693i | 0.00112584 | − | 0.00271802i | ||||
\(319\) | 13.0785i | 0.732254i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.138972 | + | 0.138972i | −0.00775664 | + | 0.00775664i | ||||
\(322\) | − | 0.725296i | − | 0.0404192i | ||||||
\(323\) | −5.43957 | + | 10.2714i | −0.302666 | + | 0.571519i | ||||
\(324\) | 16.7825 | 0.932358 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.35826 | − | 5.69333i | 0.130612 | − | 0.315325i | ||||
\(327\) | 0.279342 | 0.0154476 | ||||||||
\(328\) | 1.65923 | − | 4.00573i | 0.0916155 | − | 0.221179i | ||||
\(329\) | −0.123850 | − | 0.298999i | −0.00682805 | − | 0.0164844i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.2262 | + | 10.2262i | 0.562083 | + | 0.562083i | 0.929899 | − | 0.367816i | \(-0.119894\pi\) |
−0.367816 | + | 0.929899i | \(0.619894\pi\) | |||||||
\(332\) | −20.5966 | + | 20.5966i | −1.13038 | + | 1.13038i | ||||
\(333\) | −10.8055 | − | 26.0868i | −0.592138 | − | 1.42955i | ||||
\(334\) | −1.22045 | − | 2.94642i | −0.0667798 | − | 0.161221i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.0524633i | 0.00286211i | ||||||||
\(337\) | 22.4004 | + | 9.27853i | 1.22023 | + | 0.505434i | 0.897481 | − | 0.441052i | \(-0.145395\pi\) |
0.322744 | + | 0.946486i | \(0.395395\pi\) | |||||||
\(338\) | −2.31337 | − | 2.31337i | −0.125831 | − | 0.125831i | ||||
\(339\) | −0.596965 | −0.0324227 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.37441 | −0.453500 | ||||||||
\(342\) | −2.15218 | − | 2.15218i | −0.116377 | − | 0.116377i | ||||
\(343\) | −3.83909 | − | 1.59020i | −0.207291 | − | 0.0858629i | ||||
\(344\) | 11.4121i | 0.615300i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.64490 | + | 6.38535i | 0.142191 | + | 0.343279i | ||||
\(347\) | 8.22624 | + | 19.8599i | 0.441608 | + | 1.06614i | 0.975385 | + | 0.220510i | \(0.0707723\pi\) |
−0.533777 | + | 0.845625i | \(0.679228\pi\) | |||||||
\(348\) | −0.338981 | + | 0.338981i | −0.0181713 | + | 0.0181713i | ||||
\(349\) | 17.0669 | + | 17.0669i | 0.913570 | + | 0.913570i | 0.996551 | − | 0.0829813i | \(-0.0264442\pi\) |
−0.0829813 | + | 0.996551i | \(0.526444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.246402 | − | 0.594866i | −0.0131520 | − | 0.0317516i | ||||
\(352\) | −4.18843 | + | 10.1118i | −0.223244 | + | 0.538959i | ||||
\(353\) | 7.24444 | 0.385583 | 0.192791 | − | 0.981240i | \(-0.438246\pi\) | ||||
0.192791 | + | 0.981240i | \(0.438246\pi\) | |||||||
\(354\) | −0.0684501 | + | 0.165253i | −0.00363808 | + | 0.00878311i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.90377 | 0.153900 | ||||||||
\(357\) | 0.0196368 | + | 0.0638497i | 0.00103929 | + | 0.00337929i | ||||
\(358\) | 1.56182i | 0.0825449i | ||||||||
\(359\) | −12.2079 | + | 12.2079i | −0.644308 | + | 0.644308i | −0.951612 | − | 0.307303i | \(-0.900573\pi\) |
0.307303 | + | 0.951612i | \(0.400573\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0534i | 0.581760i | ||||||||
\(362\) | 3.27816 | − | 7.91419i | 0.172296 | − | 0.415960i | ||||
\(363\) | 0.167465 | − | 0.0693663i | 0.00878964 | − | 0.00364079i | ||||
\(364\) | −1.02173 | + | 0.423215i | −0.0535533 | + | 0.0221825i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.154658 | + | 0.154658i | 0.00808413 | + | 0.00808413i | ||||
\(367\) | −14.3289 | − | 34.5930i | −0.747963 | − | 1.80574i | −0.569883 | − | 0.821726i | \(-0.693011\pi\) |
−0.178080 | − | 0.984016i | \(-0.556989\pi\) | |||||||
\(368\) | −20.1630 | + | 8.35180i | −1.05107 | + | 0.435368i | ||||
\(369\) | −8.61057 | − | 3.56661i | −0.448248 | − | 0.185671i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.306934 | + | 0.741005i | −0.0159352 | + | 0.0384711i | ||||
\(372\) | −0.217056 | − | 0.217056i | −0.0112538 | − | 0.0112538i | ||||
\(373\) | 29.8887i | 1.54758i | 0.633443 | + | 0.773789i | \(0.281641\pi\) | ||||
−0.633443 | + | 0.773789i | \(0.718359\pi\) | |||||||
\(374\) | −0.387176 | + | 4.09219i | −0.0200204 | + | 0.211602i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.06813 | − | 1.06813i | 0.0550845 | − | 0.0550845i | ||||
\(377\) | −8.64339 | − | 3.58021i | −0.445157 | − | 0.184390i | ||||
\(378\) | −0.0350031 | −0.00180037 | ||||||||
\(379\) | 27.7353 | + | 11.4883i | 1.42467 | + | 0.590116i | 0.956028 | − | 0.293275i | \(-0.0947452\pi\) |
0.468637 | + | 0.883391i | \(0.344745\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.367412 | − | 0.152187i | 0.0188231 | − | 0.00779679i | ||||
\(382\) | −1.85209 | + | 1.85209i | −0.0947611 | + | 0.0947611i | ||||
\(383\) | −13.9465 | + | 13.9465i | −0.712634 | + | 0.712634i | −0.967086 | − | 0.254451i | \(-0.918105\pi\) |
0.254451 | + | 0.967086i | \(0.418105\pi\) | |||||||
\(384\) | −0.487556 | + | 0.201952i | −0.0248805 | + | 0.0103058i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.38861 | + | 3.06046i | 0.376070 | + | 0.155773i | ||||
\(387\) | 24.5311 | 1.24699 | ||||||||
\(388\) | −15.4995 | − | 6.42009i | −0.786866 | − | 0.325931i | ||||
\(389\) | −2.62699 | + | 2.62699i | −0.133194 | + | 0.133194i | −0.770561 | − | 0.637367i | \(-0.780024\pi\) |
0.637367 | + | 0.770561i | \(0.280024\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.4131 | + | 17.7114i | −1.08291 | + | 0.895703i | ||||
\(392\) | − | 9.63543i | − | 0.486663i | ||||||
\(393\) | 0.664326 | + | 0.664326i | 0.0335108 | + | 0.0335108i | ||||
\(394\) | 0.617821 | − | 1.49155i | 0.0311254 | − | 0.0751433i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 14.3304 | + | 5.93586i | 0.720131 | + | 0.298288i | ||||
\(397\) | −4.77812 | + | 1.97916i | −0.239807 | + | 0.0993314i | −0.499350 | − | 0.866400i | \(-0.666428\pi\) |
0.259543 | + | 0.965731i | \(0.416428\pi\) | |||||||
\(398\) | 0.0550610 | + | 0.132929i | 0.00275996 | + | 0.00666313i | ||||
\(399\) | −0.0322949 | − | 0.0322949i | −0.00161677 | − | 0.00161677i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.364698 | − | 0.151063i | 0.0182122 | − | 0.00754372i | −0.373559 | − | 0.927607i | \(-0.621863\pi\) |
0.391771 | + | 0.920063i | \(0.371863\pi\) | |||||||
\(402\) | −0.226705 | + | 0.0939042i | −0.0113070 | + | 0.00468351i | ||||
\(403\) | 2.29248 | − | 5.53453i | 0.114196 | − | 0.275695i | ||||
\(404\) | 12.9444i | 0.644007i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.359631 | + | 0.359631i | −0.0178482 | + | 0.0178482i | ||||
\(407\) | − | 26.0716i | − | 1.29232i | ||||||
\(408\) | −0.240258 | + | 0.198724i | −0.0118945 | + | 0.00983831i | ||||
\(409\) | −0.521080 | −0.0257657 | −0.0128829 | − | 0.999917i | \(-0.504101\pi\) | ||||
−0.0128829 | + | 0.999917i | \(0.504101\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.290050 | + | 0.700242i | −0.0143071 | + | 0.0345404i | ||||
\(412\) | 24.2458 | 1.19451 | ||||||||
\(413\) | 1.04647 | − | 2.52641i | 0.0514936 | − | 0.124317i | ||||
\(414\) | −2.78476 | − | 6.72301i | −0.136864 | − | 0.330418i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.53616 | − | 5.53616i | −0.271433 | − | 0.271433i | ||||
\(417\) | 0.138856 | − | 0.138856i | 0.00679981 | − | 0.00679981i | ||||
\(418\) | −1.07546 | − | 2.59640i | −0.0526026 | − | 0.126994i | ||||
\(419\) | −1.74972 | − | 4.22419i | −0.0854793 | − | 0.206365i | 0.875360 | − | 0.483472i | \(-0.160624\pi\) |
−0.960839 | + | 0.277107i | \(0.910624\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.55233i | 0.368078i | 0.982919 | + | 0.184039i | \(0.0589173\pi\) | ||||
−0.982919 | + | 0.184039i | \(0.941083\pi\) | |||||||
\(422\) | −0.649075 | − | 0.268856i | −0.0315965 | − | 0.0130877i | ||||
\(423\) | −2.29601 | − | 2.29601i | −0.111636 | − | 0.111636i | ||||
\(424\) | −3.74359 | −0.181805 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.115043 | −0.00557383 | ||||||||
\(427\) | −2.36444 | − | 2.36444i | −0.114423 | − | 0.114423i | ||||
\(428\) | 6.26110 | + | 2.59343i | 0.302642 | + | 0.125358i | ||||
\(429\) | − | 0.297114i | − | 0.0143448i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.99371 | + | 19.2985i | 0.385043 | + | 0.929577i | 0.990973 | + | 0.134059i | \(0.0428011\pi\) |
−0.605930 | + | 0.795518i | \(0.707199\pi\) | |||||||
\(432\) | 0.403062 | + | 0.973078i | 0.0193923 | + | 0.0468172i | ||||
\(433\) | −23.2292 | + | 23.2292i | −1.11632 | + | 1.11632i | −0.124045 | + | 0.992277i | \(0.539587\pi\) |
−0.992277 | + | 0.124045i | \(0.960413\pi\) | |||||||
\(434\) | −0.230279 | − | 0.230279i | −0.0110537 | − | 0.0110537i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.68612 | − | 8.89909i | −0.176533 | − | 0.426189i | ||||
\(437\) | 7.27065 | − | 17.5529i | 0.347803 | − | 0.839670i | ||||
\(438\) | 0.00423348 | 0.000202284 | ||||||||
\(439\) | −9.19069 | + | 22.1883i | −0.438648 | + | 1.05899i | 0.537769 | + | 0.843093i | \(0.319267\pi\) |
−0.976416 | + | 0.215897i | \(0.930733\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.7120 | −0.986284 | ||||||||
\(442\) | −2.59848 | − | 1.37611i | −0.123597 | − | 0.0654547i | ||||
\(443\) | 8.36893i | 0.397620i | 0.980038 | + | 0.198810i | \(0.0637077\pi\) | ||||
−0.980038 | + | 0.198810i | \(0.936292\pi\) | |||||||
\(444\) | 0.675748 | − | 0.675748i | 0.0320696 | − | 0.0320696i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.54904i | 0.404809i | ||||||||
\(447\) | 0.266876 | − | 0.644296i | 0.0126228 | − | 0.0304741i | ||||
\(448\) | 1.39410 | − | 0.577454i | 0.0658649 | − | 0.0272821i | ||||
\(449\) | −22.7241 | + | 9.41265i | −1.07242 | + | 0.444210i | −0.847844 | − | 0.530246i | \(-0.822099\pi\) |
−0.224575 | + | 0.974457i | \(0.572099\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.08503 | − | 6.08503i | −0.286533 | − | 0.286533i | ||||
\(452\) | 7.87740 | + | 19.0177i | 0.370522 | + | 0.894518i | ||||
\(453\) | 0.960292 | − | 0.397766i | 0.0451184 | − | 0.0186887i | ||||
\(454\) | 6.84296 | + | 2.83444i | 0.321156 | + | 0.133027i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0815778 | − | 0.196946i | 0.00382023 | − | 0.00922285i | ||||
\(457\) | −5.38146 | − | 5.38146i | −0.251734 | − | 0.251734i | 0.569947 | − | 0.821681i | \(-0.306964\pi\) |
−0.821681 | + | 0.569947i | \(0.806964\pi\) | |||||||
\(458\) | − | 9.58151i | − | 0.447715i | ||||||
\(459\) | 0.854760 | + | 1.03341i | 0.0398968 | + | 0.0482353i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.10577 | − | 5.10577i | 0.237800 | − | 0.237800i | −0.578139 | − | 0.815938i | \(-0.696221\pi\) |
0.815938 | + | 0.578139i | \(0.196221\pi\) | |||||||
\(462\) | −0.0149225 | − | 0.00618109i | −0.000694256 | − | 0.000287570i | ||||
\(463\) | −23.0362 | −1.07058 | −0.535292 | − | 0.844667i | \(-0.679798\pi\) | ||||
−0.535292 | + | 0.844667i | \(0.679798\pi\) | |||||||
\(464\) | 14.1388 | + | 5.85648i | 0.656377 | + | 0.271880i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.82128 | − | 3.23968i | 0.362314 | − | 0.150075i | ||||
\(467\) | −21.1457 | + | 21.1457i | −0.978506 | + | 0.978506i | −0.999774 | − | 0.0212676i | \(-0.993230\pi\) |
0.0212676 | + | 0.999774i | \(0.493230\pi\) | |||||||
\(468\) | −7.84585 | + | 7.84585i | −0.362675 | + | 0.362675i | ||||
\(469\) | 3.46589 | − | 1.43562i | 0.160040 | − | 0.0662907i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.135405 | + | 0.0560865i | 0.00623912 | + | 0.00258433i | ||||
\(472\) | 12.7636 | 0.587491 | ||||||||
\(473\) | 20.9264 | + | 8.66798i | 0.962195 | + | 0.398554i | ||||
\(474\) | −0.147221 | + | 0.147221i | −0.00676207 | + | 0.00676207i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.77496 | − | 1.46812i | 0.0813552 | − | 0.0672912i | ||||
\(477\) | 8.04710i | 0.368451i | ||||||||
\(478\) | −1.33925 | − | 1.33925i | −0.0612561 | − | 0.0612561i | ||||
\(479\) | −3.69569 | + | 8.92218i | −0.168860 | + | 0.407665i | −0.985544 | − | 0.169421i | \(-0.945810\pi\) |
0.816684 | + | 0.577086i | \(0.195810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.2303 | + | 7.13704i | 0.785636 | + | 0.325421i | ||||
\(482\) | 1.81031 | − | 0.749855i | 0.0824574 | − | 0.0341550i | ||||
\(483\) | −0.0417872 | − | 0.100883i | −0.00190138 | − | 0.00459035i | ||||
\(484\) | −4.41965 | − | 4.41965i | −0.200893 | − | 0.200893i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.486764 | + | 0.201624i | −0.0220801 | + | 0.00914586i | ||||
\(487\) | −4.46244 | + | 1.84840i | −0.202212 | + | 0.0837591i | −0.481491 | − | 0.876451i | \(-0.659905\pi\) |
0.279279 | + | 0.960210i | \(0.409905\pi\) | |||||||
\(488\) | 5.97263 | − | 14.4192i | 0.270368 | − | 0.652727i | ||||
\(489\) | − | 0.927769i | − | 0.0419552i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.1849 | − | 15.1849i | 0.685287 | − | 0.685287i | −0.275900 | − | 0.961186i | \(-0.588976\pi\) |
0.961186 | + | 0.275900i | \(0.0889758\pi\) | |||||||
\(492\) | − | 0.315436i | − | 0.0142209i | ||||||
\(493\) | 19.3995 | + | 1.83545i | 0.873708 | + | 0.0826646i | ||||
\(494\) | 2.01033 | 0.0904490 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.75002 | + | 9.05334i | −0.168381 | + | 0.406507i | ||||
\(497\) | 1.75879 | 0.0788923 | ||||||||
\(498\) | 0.116457 | − | 0.281152i | 0.00521856 | − | 0.0125987i | ||||
\(499\) | 7.13250 | + | 17.2194i | 0.319295 | + | 0.770845i | 0.999292 | + | 0.0376305i | \(0.0119810\pi\) |
−0.679997 | + | 0.733215i | \(0.738019\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.339510 | − | 0.339510i | −0.0151682 | − | 0.0151682i | ||||
\(502\) | −6.72164 | + | 6.72164i | −0.300001 | + | 0.300001i | ||||
\(503\) | −7.10981 | − | 17.1646i | −0.317011 | − | 0.765332i | −0.999410 | − | 0.0343519i | \(-0.989063\pi\) |
0.682399 | − | 0.730980i | \(-0.260937\pi\) | |||||||
\(504\) | 0.477685 | + | 1.15323i | 0.0212778 | + | 0.0513691i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 6.71908i | − | 0.298700i | ||||||
\(507\) | −0.455055 | − | 0.188490i | −0.0202097 | − | 0.00837113i | ||||
\(508\) | −9.69656 | − | 9.69656i | −0.430215 | − | 0.430215i | ||||
\(509\) | 28.4343 | 1.26033 | 0.630163 | − | 0.776463i | \(-0.282988\pi\) | ||||
0.630163 | + | 0.776463i | \(0.282988\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0647220 | −0.00286313 | ||||||||
\(512\) | 15.4409 | + | 15.4409i | 0.682399 | + | 0.682399i | ||||
\(513\) | −0.847112 | − | 0.350885i | −0.0374009 | − | 0.0154920i | ||||
\(514\) | − | 6.75508i | − | 0.297954i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.317725 | + | 0.767056i | 0.0139871 | + | 0.0337677i | ||||
\(517\) | −1.14733 | − | 2.76991i | −0.0504597 | − | 0.121820i | ||||
\(518\) | 0.716913 | − | 0.716913i | 0.0314993 | − | 0.0314993i | ||||
\(519\) | 0.735771 | + | 0.735771i | 0.0322968 | + | 0.0322968i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.26078 | − | 17.5291i | −0.318100 | − | 0.767962i | −0.999355 | − | 0.0359155i | \(-0.988565\pi\) |
0.681254 | − | 0.732047i | \(-0.261435\pi\) | |||||||
\(522\) | −1.95274 | + | 4.71434i | −0.0854692 | + | 0.206341i | ||||
\(523\) | 24.4504 | 1.06914 | 0.534571 | − | 0.845124i | \(-0.320473\pi\) | ||||
0.534571 | + | 0.845124i | \(0.320473\pi\) | |||||||
\(524\) | 12.3974 | − | 29.9299i | 0.541583 | − | 1.30750i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.76445 | −0.251342 | ||||||||
\(527\) | −1.17528 | + | 12.4219i | −0.0511958 | + | 0.541105i | ||||
\(528\) | 0.486016i | 0.0211511i | ||||||||
\(529\) | 15.8564 | − | 15.8564i | 0.689407 | − | 0.689407i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 27.4361i | − | 1.19063i | ||||||
\(532\) | −0.602675 | + | 1.45499i | −0.0261293 | + | 0.0630816i | ||||
\(533\) | 5.68728 | − | 2.35575i | 0.246344 | − | 0.102039i | ||||
\(534\) | −0.0280281 | + | 0.0116096i | −0.00121289 | + | 0.000502397i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.3813 | + | 12.3813i | 0.534792 | + | 0.534792i | ||||
\(537\) | 0.0899828 | + | 0.217238i | 0.00388305 | + | 0.00937450i | ||||
\(538\) | −0.398194 | + | 0.164937i | −0.0171674 | + | 0.00711096i | ||||
\(539\) | −17.6684 | − | 7.31851i | −0.761034 | − | 0.315230i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.13701 | + | 9.98762i | −0.177864 | + | 0.429401i | −0.987518 | − | 0.157506i | \(-0.949655\pi\) |
0.809654 | + | 0.586907i | \(0.199655\pi\) | |||||||
\(542\) | −0.226358 | − | 0.226358i | −0.00972291 | − | 0.00972291i | ||||
\(543\) | − | 1.28967i | − | 0.0553451i | ||||||
\(544\) | 14.4111 | + | 7.63186i | 0.617871 | + | 0.327213i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.00817000 | − | 0.00817000i | 0.000349644 | − | 0.000349644i | ||||
\(547\) | 6.71889 | + | 2.78305i | 0.287279 | + | 0.118995i | 0.521669 | − | 0.853148i | \(-0.325309\pi\) |
−0.234391 | + | 0.972143i | \(0.575309\pi\) | |||||||
\(548\) | 26.1353 | 1.11644 | ||||||||
\(549\) | −30.9950 | − | 12.8386i | −1.32284 | − | 0.547937i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.3085 | + | 5.09835i | −0.524360 | + | 0.217197i | ||||
\(552\) | 0.360389 | − | 0.360389i | 0.0153392 | − | 0.0153392i | ||||
\(553\) | 2.25073 | − | 2.25073i | 0.0957108 | − | 0.0957108i | ||||
\(554\) | −2.05648 | + | 0.851821i | −0.0873714 | + | 0.0361904i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.25589 | − | 2.59128i | −0.265309 | − | 0.109895i | ||||
\(557\) | −18.3930 | −0.779335 | −0.389667 | − | 0.920956i | \(-0.627410\pi\) | ||||
−0.389667 | + | 0.920956i | \(0.627410\pi\) | |||||||
\(558\) | −3.01868 | − | 1.25038i | −0.127791 | − | 0.0529328i | ||||
\(559\) | −11.4571 | + | 11.4571i | −0.484584 | + | 0.484584i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.181914 | + | 0.591499i | 0.00768041 | + | 0.0249731i | ||||
\(562\) | − | 10.0495i | − | 0.423911i | ||||||
\(563\) | 0.317586 | + | 0.317586i | 0.0133847 | + | 0.0133847i | 0.713767 | − | 0.700383i | \(-0.246987\pi\) |
−0.700383 | + | 0.713767i | \(0.746987\pi\) | |||||||
\(564\) | 0.0420555 | − | 0.101531i | 0.00177086 | − | 0.00427522i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.88909 | − | 4.09620i | −0.415670 | − | 0.172176i | ||||
\(567\) | 2.47651 | − | 1.02581i | 0.104004 | − | 0.0430798i | ||||
\(568\) | 3.14149 | + | 7.58423i | 0.131814 | + | 0.318227i | ||||
\(569\) | −10.1299 | − | 10.1299i | −0.424669 | − | 0.424669i | 0.462138 | − | 0.886808i | \(-0.347082\pi\) |
−0.886808 | + | 0.462138i | \(0.847082\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.8617 | − | 10.7123i | 1.08228 | − | 0.448294i | 0.230970 | − | 0.972961i | \(-0.425810\pi\) |
0.851307 | + | 0.524667i | \(0.175810\pi\) | |||||||
\(572\) | −9.46525 | + | 3.92063i | −0.395762 | + | 0.163930i | ||||
\(573\) | −0.150905 | + | 0.364318i | −0.00630417 | + | 0.0152196i | ||||
\(574\) | − | 0.334651i | − | 0.0139681i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 10.7052 | − | 10.7052i | 0.446052 | − | 0.446052i | ||||
\(577\) | 6.76924i | 0.281807i | 0.990023 | + | 0.140904i | \(0.0450008\pi\) | ||||
−0.990023 | + | 0.140904i | \(0.954999\pi\) | |||||||
\(578\) | 6.01565 | + | 1.14861i | 0.250218 | + | 0.0477757i | ||||
\(579\) | 1.20403 | 0.0500376 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.78041 | + | 4.29829i | −0.0738638 | + | 0.178323i | ||||
\(582\) | 0.175274 | 0.00726533 | ||||||||
\(583\) | −2.84342 | + | 6.86461i | −0.117762 | + | 0.284303i | ||||
\(584\) | −0.115605 | − | 0.279094i | −0.00478375 | − | 0.0115490i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.72209 | + | 5.72209i | 0.236377 | + | 0.236377i | ||||
\(587\) | 17.4713 | − | 17.4713i | 0.721117 | − | 0.721117i | −0.247715 | − | 0.968833i | \(-0.579680\pi\) |
0.968833 | + | 0.247715i | \(0.0796798\pi\) | |||||||
\(588\) | −0.268260 | − | 0.647637i | −0.0110628 | − | 0.0267081i | ||||
\(589\) | −3.26458 | − | 7.88139i | −0.134515 | − | 0.324747i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 0.243059i | − | 0.00999810i | ||||||
\(592\) | −28.1852 | − | 11.6747i | −1.15841 | − | 0.479828i | ||||
\(593\) | −15.8749 | − | 15.8749i | −0.651905 | − | 0.651905i | 0.301547 | − | 0.953451i | \(-0.402497\pi\) |
−0.953451 | + | 0.301547i | \(0.902497\pi\) | |||||||
\(594\) | −0.324266 | −0.0133048 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −24.0472 | −0.985010 | ||||||||
\(597\) | 0.0153172 | + | 0.0153172i | 0.000626889 | + | 0.000626889i | ||||
\(598\) | 4.44055 | + | 1.83934i | 0.181588 | + | 0.0752161i | ||||
\(599\) | − | 19.1639i | − | 0.783018i | −0.920174 | − | 0.391509i | \(-0.871953\pi\) | ||
0.920174 | − | 0.391509i | \(-0.128047\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.87947 | − | 21.4369i | −0.362201 | − | 0.874431i | −0.994978 | − | 0.100096i | \(-0.968085\pi\) |
0.632777 | − | 0.774334i | \(-0.281915\pi\) | |||||||
\(602\) | 0.337080 | + | 0.813782i | 0.0137383 | + | 0.0331673i | ||||
\(603\) | 26.6145 | − | 26.6145i | 1.08383 | − | 1.08383i | ||||
\(604\) | −25.3435 | − | 25.3435i | −1.03121 | − | 1.03121i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.0517530 | − | 0.124943i | −0.00210232 | − | 0.00507546i | ||||
\(607\) | 0.713459 | − | 1.72244i | 0.0289584 | − | 0.0699118i | −0.908739 | − | 0.417365i | \(-0.862954\pi\) |
0.937697 | + | 0.347454i | \(0.112954\pi\) | |||||||
\(608\) | −11.1492 | −0.452161 | ||||||||
\(609\) | −0.0293022 | + | 0.0707417i | −0.00118738 | + | 0.00286660i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.14468 | 0.0867643 | ||||||||
\(612\) | 10.8159 | − | 20.4235i | 0.437206 | − | 0.825569i | ||||
\(613\) | − | 0.383092i | − | 0.0154729i | −0.999970 | − | 0.00773647i | \(-0.997537\pi\) | ||
0.999970 | − | 0.00773647i | \(-0.00246262\pi\) | |||||||
\(614\) | 1.41088 | − | 1.41088i | 0.0569384 | − | 0.0569384i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.15256i | 0.0464379i | ||||||||
\(617\) | 4.46499 | − | 10.7794i | 0.179754 | − | 0.433964i | −0.808161 | − | 0.588962i | \(-0.799537\pi\) |
0.987915 | + | 0.154997i | \(0.0495370\pi\) | |||||||
\(618\) | −0.234028 | + | 0.0969375i | −0.00941398 | + | 0.00389940i | ||||
\(619\) | 12.4590 | − | 5.16070i | 0.500771 | − | 0.207426i | −0.117976 | − | 0.993016i | \(-0.537641\pi\) |
0.618747 | + | 0.785590i | \(0.287641\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.55012 | − | 1.55012i | −0.0622041 | − | 0.0622041i | ||||
\(622\) | −3.11143 | − | 7.51165i | −0.124757 | − | 0.301190i | ||||
\(623\) | 0.428497 | − | 0.177489i | 0.0171674 | − | 0.00711096i | ||||
\(624\) | −0.321201 | − | 0.133046i | −0.0128583 | − | 0.00532610i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.67996 | − | 4.05578i | 0.0671446 | − | 0.162101i | ||||
\(627\) | −0.299178 | − | 0.299178i | −0.0119480 | − | 0.0119480i | ||||
\(628\) | − | 5.05373i | − | 0.201666i | ||||||
\(629\) | −38.6723 | − | 3.65892i | −1.54196 | − | 0.145891i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.1913 | + | 33.1913i | −1.32132 | + | 1.32132i | −0.408617 | + | 0.912706i | \(0.633989\pi\) |
−0.912706 | + | 0.408617i | \(0.866011\pi\) | |||||||
\(632\) | 13.7258 | + | 5.68540i | 0.545982 | + | 0.226153i | ||||
\(633\) | −0.105771 | −0.00420403 | ||||||||
\(634\) | −7.31470 | − | 3.02985i | −0.290504 | − | 0.120331i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.251622 | + | 0.104225i | −0.00997747 | + | 0.00413280i | ||||
\(637\) | 9.67341 | − | 9.67341i | 0.383274 | − | 0.383274i | ||||
\(638\) | −3.33159 | + | 3.33159i | −0.131899 | + | 0.131899i | ||||
\(639\) | 16.3028 | − | 6.75284i | 0.644928 | − | 0.267138i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.5657 | + | 15.1460i | 1.44426 | + | 0.598232i | 0.960827 | − | 0.277150i | \(-0.0893898\pi\) |
0.483433 | + | 0.875382i | \(0.339390\pi\) | |||||||
\(642\) | −0.0708028 | −0.00279436 | ||||||||
\(643\) | 16.3686 | + | 6.78010i | 0.645515 | + | 0.267381i | 0.681329 | − | 0.731978i | \(-0.261402\pi\) |
−0.0358141 | + | 0.999358i | \(0.511402\pi\) | |||||||
\(644\) | −2.66246 | + | 2.66246i | −0.104916 | + | 0.104916i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.00220 | + | 1.23087i | −0.157464 | + | 0.0484278i | ||||
\(647\) | 14.8304i | 0.583045i | 0.956564 | + | 0.291522i | \(0.0941618\pi\) | ||||
−0.956564 | + | 0.291522i | \(0.905838\pi\) | |||||||
\(648\) | 8.84694 | + | 8.84694i | 0.347541 | + | 0.347541i | ||||
\(649\) | 9.69446 | − | 23.4045i | 0.380541 | − | 0.918707i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0452973 | − | 0.0187628i | −0.00177534 | − | 0.000735370i | ||||
\(652\) | −29.5562 | + | 12.2426i | −1.15751 | + | 0.479457i | ||||
\(653\) | 3.90283 | + | 9.42227i | 0.152730 | + | 0.368722i | 0.981663 | − | 0.190626i | \(-0.0610517\pi\) |
−0.828933 | + | 0.559348i | \(0.811052\pi\) | |||||||
\(654\) | 0.0711591 | + | 0.0711591i | 0.00278254 | + | 0.00278254i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.30321 | + | 3.85352i | −0.363229 | + | 0.150455i | ||||
\(657\) | −0.599931 | + | 0.248499i | −0.0234055 | + | 0.00969488i | ||||
\(658\) | 0.0446174 | − | 0.107716i | 0.00173937 | − | 0.00419920i | ||||
\(659\) | − | 45.4453i | − | 1.77030i | −0.465309 | − | 0.885148i | \(-0.654057\pi\) | ||
0.465309 | − | 0.885148i | \(-0.345943\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.62214 | + | 5.62214i | −0.218676 | + | 0.218676i | −0.807940 | − | 0.589264i | \(-0.799418\pi\) |
0.589264 | + | 0.807940i | \(0.299418\pi\) | |||||||
\(662\) | 5.21001i | 0.202493i | ||||||||
\(663\) | −0.440712 | − | 0.0416973i | −0.0171158 | − | 0.00161939i | ||||
\(664\) | −21.7152 | −0.842712 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.89273 | − | 9.39789i | 0.150840 | − | 0.364161i | ||||
\(667\) | −31.8526 | −1.23334 | ||||||||
\(668\) | −6.33579 | + | 15.2960i | −0.245139 | + | 0.591818i | ||||
\(669\) | 0.492545 | + | 1.18911i | 0.0190429 | + | 0.0459736i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.9040 | − | 21.9040i | −0.845594 | − | 0.845594i | ||||
\(672\) | −0.0453106 | + | 0.0453106i | −0.00174789 | + | 0.00174789i | ||||
\(673\) | 8.41428 | + | 20.3139i | 0.324347 | + | 0.783042i | 0.998992 | + | 0.0448994i | \(0.0142967\pi\) |
−0.674645 | + | 0.738142i | \(0.735703\pi\) | |||||||
\(674\) | 3.34263 | + | 8.06983i | 0.128753 | + | 0.310838i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.9841i | 0.653234i | ||||||||
\(677\) | 16.8488 | + | 6.97899i | 0.647551 | + | 0.268224i | 0.682189 | − | 0.731176i | \(-0.261028\pi\) |
−0.0346387 | + | 0.999400i | \(0.511028\pi\) | |||||||
\(678\) | −0.152070 | − | 0.152070i | −0.00584021 | − | 0.00584021i | ||||
\(679\) | −2.67961 | −0.102834 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.11511 | 0.0427310 | ||||||||
\(682\) | −2.13328 | − | 2.13328i | −0.0816876 | − | 0.0816876i | ||||
\(683\) | −16.8175 | − | 6.96604i | −0.643504 | − | 0.266548i | 0.0369746 | − | 0.999316i | \(-0.488228\pi\) |
−0.680478 | + | 0.732768i | \(0.738228\pi\) | |||||||
\(684\) | 15.8007i | 0.604156i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.572878 | − | 1.38305i | −0.0218726 | − | 0.0528051i | ||||
\(687\) | −0.552029 | − | 1.33272i | −0.0210612 | − | 0.0508463i | ||||
\(688\) | 18.7414 | − | 18.7414i | 0.714511 | − | 0.714511i | ||||
\(689\) | −3.75835 | − | 3.75835i | −0.143182 | − | 0.143182i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.95556 | + | 14.3780i | 0.226560 | + | 0.546965i | 0.995754 | − | 0.0920503i | \(-0.0293421\pi\) |
−0.769194 | + | 0.639015i | \(0.779342\pi\) | |||||||
\(692\) | 13.7307 | − | 33.1488i | 0.521962 | − | 1.26013i | ||||
\(693\) | 2.47750 | 0.0941124 | ||||||||
\(694\) | −2.96354 | + | 7.15462i | −0.112494 | + | 0.271586i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.357391 | −0.0135469 | ||||||||
\(697\) | −9.87999 | + | 8.17202i | −0.374231 | + | 0.309537i | ||||
\(698\) | 8.69519i | 0.329118i | ||||||||
\(699\) | 0.901230 | − | 0.901230i | 0.0340876 | − | 0.0340876i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8.07561i | − | 0.305011i | −0.988303 | − | 0.152506i | \(-0.951266\pi\) | ||
0.988303 | − | 0.152506i | \(-0.0487342\pi\) | |||||||
\(702\) | 0.0887673 | − | 0.214303i | 0.00335031 | − | 0.00808836i | ||||
\(703\) | 24.5367 | − | 10.1634i | 0.925417 | − | 0.383320i | ||||
\(704\) | 12.9148 | − | 5.34949i | 0.486745 | − | 0.201617i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.84544 | + | 1.84544i | 0.0694540 | + | 0.0694540i | ||||
\(707\) | 0.791208 | + | 1.91014i | 0.0297564 | + | 0.0718384i | ||||
\(708\) | 0.857891 | − | 0.355350i | 0.0322415 | − | 0.0133549i | ||||
\(709\) | 4.88749 | + | 2.02447i | 0.183554 | + | 0.0760304i | 0.472567 | − | 0.881295i | \(-0.343327\pi\) |
−0.289014 | + | 0.957325i | \(0.593327\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.2211 | − | 29.5044i | 0.458329 | − | 1.10650i | ||||
\(712\) | 1.53074 | + | 1.53074i | 0.0573668 | + | 0.0573668i | ||||
\(713\) | − | 20.3958i | − | 0.763830i | ||||||
\(714\) | −0.0112627 | + | 0.0212672i | −0.000421497 | + | 0.000795906i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.73323 | − | 5.73323i | 0.214261 | − | 0.214261i | ||||
\(717\) | −0.263440 | − | 0.109120i | −0.00983835 | − | 0.00407518i | ||||
\(718\) | −6.21964 | −0.232115 | ||||||||
\(719\) | 8.27731 | + | 3.42857i | 0.308691 | + | 0.127864i | 0.531651 | − | 0.846964i | \(-0.321572\pi\) |
−0.222960 | + | 0.974828i | \(0.571572\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.57785 | − | 1.48199i | 0.133246 | − | 0.0551923i | ||||
\(722\) | −2.81573 | + | 2.81573i | −0.104791 | + | 0.104791i | ||||
\(723\) | 0.208598 | − | 0.208598i | 0.00775786 | − | 0.00775786i | ||||
\(724\) | −41.0855 | + | 17.0182i | −1.52693 | + | 0.632476i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.0603301 | + | 0.0249895i | 0.00223906 | + | 0.000927449i | ||||
\(727\) | −29.9868 | −1.11215 | −0.556074 | − | 0.831133i | \(-0.687693\pi\) | ||||
−0.556074 | + | 0.831133i | \(0.687693\pi\) | |||||||
\(728\) | −0.761710 | − | 0.315511i | −0.0282309 | − | 0.0116936i | ||||
\(729\) | 18.9797 | − | 18.9797i | 0.702950 | − | 0.702950i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.7942 | − | 29.8239i | 0.584168 | − | 1.10308i | ||||
\(732\) | − | 1.13546i | − | 0.0419678i | ||||||
\(733\) | −19.0696 | − | 19.0696i | −0.704352 | − | 0.704352i | 0.260990 | − | 0.965342i | \(-0.415951\pi\) |
−0.965342 | + | 0.260990i | \(0.915951\pi\) | |||||||
\(734\) | 5.16205 | − | 12.4623i | 0.190535 | − | 0.459992i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.6272 | − | 10.2009i | −0.907770 | − | 0.376011i | ||||
\(737\) | 32.1078 | − | 13.2995i | 1.18270 | − | 0.489892i | ||||
\(738\) | −1.28489 | − | 3.10200i | −0.0472974 | − | 0.114186i | ||||
\(739\) | 24.6401 | + | 24.6401i | 0.906400 | + | 0.906400i | 0.995980 | − | 0.0895798i | \(-0.0285524\pi\) |
−0.0895798 | + | 0.995980i | \(0.528552\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.279622 | − | 0.115823i | 0.0102722 | − | 0.00425487i | ||||
\(742\) | −0.266950 | + | 0.110574i | −0.00980006 | + | 0.00405932i | ||||
\(743\) | 6.54116 | − | 15.7918i | 0.239972 | − | 0.579344i | −0.757307 | − | 0.653059i | \(-0.773486\pi\) |
0.997279 | + | 0.0737150i | \(0.0234855\pi\) | |||||||
\(744\) | − | 0.228844i | − | 0.00838984i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.61380 | + | 7.61380i | −0.278761 | + | 0.278761i | ||||
\(747\) | 46.6781i | 1.70786i | ||||||||
\(748\) | 16.4431 | − | 13.6006i | 0.601219 | − | 0.497286i | ||||
\(749\) | 1.08244 | 0.0395516 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.5831 | + | 30.3783i | −0.459165 | + | 1.10852i | 0.509572 | + | 0.860428i | \(0.329804\pi\) |
−0.968736 | + | 0.248093i | \(0.920196\pi\) | |||||||
\(752\) | −3.50824 | −0.127932 | ||||||||
\(753\) | −0.547669 | + | 1.32219i | −0.0199582 | + | 0.0481833i | ||||
\(754\) | −1.28979 | − | 3.11382i | −0.0469713 | − | 0.113399i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.128492 | + | 0.128492i | 0.00467319 | + | 0.00467319i | ||||
\(757\) | 12.3728 | − | 12.3728i | 0.449698 | − | 0.449698i | −0.445556 | − | 0.895254i | \(-0.646994\pi\) |
0.895254 | + | 0.445556i | \(0.146994\pi\) | |||||||
\(758\) | 4.13872 | + | 9.99176i | 0.150325 | + | 0.362917i | ||||
\(759\) | −0.387113 | − | 0.934574i | −0.0140513 | − | 0.0339229i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 10.8439i | − | 0.393092i | −0.980495 | − | 0.196546i | \(-0.937028\pi\) | ||
0.980495 | − | 0.196546i | \(-0.0629724\pi\) | |||||||
\(762\) | 0.132362 | + | 0.0548261i | 0.00479497 | + | 0.00198614i | ||||
\(763\) | −1.08789 | − | 1.08789i | −0.0393843 | − | 0.0393843i | ||||
\(764\) | 13.5975 | 0.491941 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.10543 | −0.256730 | ||||||||
\(767\) | 12.8139 | + | 12.8139i | 0.462682 | + | 0.462682i | ||||
\(768\) | 0.330599 | + | 0.136939i | 0.0119295 | + | 0.00494135i | ||||
\(769\) | 14.8775i | 0.536497i | 0.963350 | + | 0.268248i | \(0.0864448\pi\) | ||||
−0.963350 | + | 0.268248i | \(0.913555\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.389187 | − | 0.939581i | −0.0140162 | − | 0.0338382i | ||||
\(772\) | −15.8880 | − | 38.3571i | −0.571822 | − | 1.38050i | ||||
\(773\) | −5.45537 | + | 5.45537i | −0.196216 | + | 0.196216i | −0.798376 | − | 0.602160i | \(-0.794307\pi\) |
0.602160 | + | 0.798376i | \(0.294307\pi\) | |||||||
\(774\) | 6.24901 | + | 6.24901i | 0.224616 | + | 0.224616i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.78623 | − | 11.5550i | −0.171816 | − | 0.414800i | ||||
\(777\) | 0.0584130 | − | 0.141021i | 0.00209555 | − | 0.00505912i | ||||
\(778\) | −1.33839 | −0.0479836 | ||||||||
\(779\) | 3.35468 | − | 8.09891i | 0.120194 | − | 0.290173i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.2933 | 0.583019 | ||||||||
\(782\) | −9.96650 | − | 0.942965i | −0.356401 | − | 0.0337204i | ||||
\(783\) | 1.53722i | 0.0549358i | ||||||||
\(784\) | −15.8237 | + | 15.8237i | −0.565131 | + | 0.565131i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.338459i | 0.0120724i | ||||||||
\(787\) | −14.6385 | + | 35.3404i | −0.521805 | + | 1.25975i | 0.414975 | + | 0.909833i | \(0.363790\pi\) |
−0.936781 | + | 0.349917i | \(0.886210\pi\) | |||||||
\(788\) | −7.74321 | + | 3.20734i | −0.275840 | + | 0.114257i | ||||
\(789\) | −0.801792 | + | 0.332113i | −0.0285446 | + | 0.0118235i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.32487 | + | 2.32487i | 0.0826627 | + | 0.0826627i | ||||
\(792\) | 4.42523 | + | 10.6835i | 0.157244 | + | 0.379620i | ||||
\(793\) | 20.4722 | − | 8.47987i | 0.726990 | − | 0.301129i | ||||
\(794\) | −1.72134 | − | 0.713003i | −0.0610881 | − | 0.0253035i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.285843 | − | 0.690085i | 0.0101314 | − | 0.0244594i | ||||
\(797\) | 18.8205 | + | 18.8205i | 0.666657 | + | 0.666657i | 0.956941 | − | 0.290284i | \(-0.0937496\pi\) |
−0.290284 | + | 0.956941i | \(0.593750\pi\) | |||||||
\(798\) | − | 0.0164535i | − | 0.000582448i | ||||||
\(799\) | −4.26966 | + | 1.31312i | −0.151050 | + | 0.0464549i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.29042 | − | 3.29042i | 0.116261 | − | 0.116261i | ||||
\(802\) | 0.131384 | + | 0.0544211i | 0.00463934 | + | 0.00192168i | ||||
\(803\) | −0.599580 | −0.0211587 | ||||||||
\(804\) | 1.17691 | + | 0.487492i | 0.0415064 | + | 0.0171925i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.99384 | − | 0.825876i | 0.0702300 | − | 0.0290902i | ||||
\(807\) | −0.0458831 | + | 0.0458831i | −0.00161516 | + | 0.00161516i | ||||
\(808\) | −6.82368 | + | 6.82368i | −0.240056 | + | 0.240056i | ||||
\(809\) | −15.1856 | + | 6.29009i | −0.533898 | + | 0.221148i | −0.633309 | − | 0.773899i | \(-0.718304\pi\) |
0.0994117 | + | 0.995046i | \(0.468304\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.36428 | − | 1.39353i | −0.118136 | − | 0.0489335i | 0.322833 | − | 0.946456i | \(-0.395365\pi\) |
−0.440968 | + | 0.897523i | \(0.645365\pi\) | |||||||
\(812\) | 2.64031 | 0.0926566 | ||||||||
\(813\) | −0.0445261 | − | 0.0184433i | −0.00156160 | − | 0.000646835i | ||||
\(814\) | 6.64143 | − | 6.64143i | 0.232782 | − | 0.232782i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.720914 | + | 0.0682081i | 0.0252370 | + | 0.00238776i | ||||
\(817\) | 23.0734i | 0.807236i | ||||||||
\(818\) | −0.132739 | − | 0.132739i | −0.00464111 | − | 0.00464111i | ||||
\(819\) | −0.678211 | + | 1.63735i | −0.0236986 | + | 0.0572135i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.8228 | + | 13.5957i | 1.14552 | + | 0.474492i | 0.873030 | − | 0.487666i | \(-0.162152\pi\) |
0.272494 | + | 0.962158i | \(0.412152\pi\) | |||||||
\(822\) | −0.252265 | + | 0.104492i | −0.00879876 | + | 0.00364457i | ||||
\(823\) | 1.91962 | + | 4.63438i | 0.0669138 | + | 0.161544i | 0.953799 | − | 0.300446i | \(-0.0971355\pi\) |
−0.886885 | + | 0.461990i | \(0.847136\pi\) | |||||||
\(824\) | 12.7813 | + | 12.7813i | 0.445257 | + | 0.445257i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.910152 | − | 0.376997i | 0.0316682 | − | 0.0131174i | ||||
\(827\) | 36.1131 | − | 14.9585i | 1.25578 | − | 0.520159i | 0.347165 | − | 0.937804i | \(-0.387144\pi\) |
0.908610 | + | 0.417645i | \(0.137144\pi\) | |||||||
\(828\) | −14.4568 | + | 34.9017i | −0.502407 | + | 1.21292i | ||||
\(829\) | 16.3998i | 0.569587i | 0.958589 | + | 0.284794i | \(0.0919250\pi\) | ||||
−0.958589 | + | 0.284794i | \(0.908075\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.236964 | + | 0.236964i | −0.00822019 | + | 0.00822019i | ||||
\(832\) | 9.99964i | 0.346675i | ||||||||
\(833\) | −13.3352 | + | 25.1807i | −0.462039 | + | 0.872461i | ||||
\(834\) | 0.0707439 | 0.00244966 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.58313 | + | 13.4789i | −0.193097 | + | 0.466177i | ||||
\(837\) | −0.984314 | −0.0340229 | ||||||||
\(838\) | 0.630344 | − | 1.52178i | 0.0217749 | − | 0.0525692i | ||||
\(839\) | 11.4471 | + | 27.6357i | 0.395197 | + | 0.954090i | 0.988788 | + | 0.149324i | \(0.0477096\pi\) |
−0.593591 | + | 0.804767i | \(0.702290\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.71231 | − | 4.71231i | −0.162493 | − | 0.162493i | ||||
\(842\) | −1.92387 | + | 1.92387i | −0.0663009 | + | 0.0663009i | ||||
\(843\) | −0.578989 | − | 1.39780i | −0.0199414 | − | 0.0481429i | ||||
\(844\) | 1.39573 | + | 3.36959i | 0.0480431 | + | 0.115986i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 1.16976i | − | 0.0402173i | ||||||
\(847\) | −0.922334 | − | 0.382043i | −0.0316918 | − | 0.0131272i | ||||
\(848\) | 6.14788 | + | 6.14788i | 0.211119 | + | 0.211119i | ||||
\(849\) | −1.61150 | −0.0553064 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 63.4972 | 2.17666 | ||||||||
\(852\) | 0.422305 | + | 0.422305i | 0.0144679 | + | 0.0144679i | ||||
\(853\) | −33.1784 | − | 13.7430i | −1.13601 | − | 0.470550i | −0.266189 | − | 0.963921i | \(-0.585765\pi\) |
−0.869819 | + | 0.493371i | \(0.835765\pi\) | |||||||
\(854\) | − | 1.20463i | − | 0.0412215i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.93343 | + | 4.66771i | 0.0660832 | + | 0.159539i | ||||
\(857\) | −8.06374 | − | 19.4676i | −0.275452 | − | 0.665000i | 0.724247 | − | 0.689541i | \(-0.242188\pi\) |
−0.999699 | + | 0.0245406i | \(0.992188\pi\) | |||||||
\(858\) | 0.0756862 | − | 0.0756862i | 0.00258389 | − | 0.00258389i | ||||
\(859\) | 11.2104 | + | 11.2104i | 0.382494 | + | 0.382494i | 0.872000 | − | 0.489506i | \(-0.162823\pi\) |
−0.489506 | + | 0.872000i | \(0.662823\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0192806 | − | 0.0465475i | −0.000657081 | − | 0.00158633i | ||||
\(862\) | −2.87977 | + | 6.95238i | −0.0980853 | + | 0.236799i | ||||
\(863\) | −23.8125 | −0.810587 | −0.405294 | − | 0.914187i | \(-0.632831\pi\) | ||||
−0.405294 | + | 0.914187i | \(0.632831\pi\) | |||||||
\(864\) | −0.492301 | + | 1.18852i | −0.0167484 | + | 0.0404343i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.8347 | −0.402160 | ||||||||
\(867\) | 0.902908 | − | 0.186823i | 0.0306644 | − | 0.00634486i | ||||
\(868\) | 1.69064i | 0.0573841i | ||||||||
\(869\) | 20.8506 | − | 20.8506i | 0.707308 | − | 0.707308i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.8603i | 0.842359i | ||||||||
\(872\) | 2.74804 | − | 6.63435i | 0.0930603 | − | 0.224667i | ||||
\(873\) | −24.8382 | + | 10.2883i | −0.840645 | + | 0.348207i | ||||
\(874\) | 6.32351 | − | 2.61929i | 0.213896 | − | 0.0885987i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.0155405 | − | 0.0155405i | −0.000525065 | − | 0.000525065i | ||||
\(877\) | −6.85759 | − | 16.5557i | −0.231564 | − | 0.559046i | 0.764797 | − | 0.644271i | \(-0.222839\pi\) |
−0.996362 | + | 0.0852252i | \(0.972839\pi\) | |||||||
\(878\) | −7.99343 | + | 3.31099i | −0.269765 | + | 0.111740i | ||||
\(879\) | 1.12557 | + | 0.466228i | 0.0379646 | + | 0.0157255i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.9301 | + | 31.2159i | −0.435625 | + | 1.05169i | 0.541819 | + | 0.840495i | \(0.317736\pi\) |
−0.977444 | + | 0.211196i | \(0.932264\pi\) | |||||||
\(882\) | −5.27613 | − | 5.27613i | −0.177657 | − | 0.177657i | ||||
\(883\) | 26.0211i | 0.875680i | 0.899053 | + | 0.437840i | \(0.144256\pi\) | ||||
−0.899053 | + | 0.437840i | \(0.855744\pi\) | |||||||
\(884\) | 4.48716 | + | 14.5901i | 0.150920 | + | 0.490720i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.13189 | + | 2.13189i | −0.0716222 | + | 0.0716222i | ||||
\(887\) | 27.3959 | + | 11.3477i | 0.919863 | + | 0.381020i | 0.791824 | − | 0.610749i | \(-0.209132\pi\) |
0.128039 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(888\) | 0.712447 | 0.0239082 | ||||||||
\(889\) | −2.02357 | − | 0.838189i | −0.0678683 | − | 0.0281120i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.9422 | − | 9.50298i | 0.768593 | − | 0.318362i | ||||
\(892\) | 31.3823 | − | 31.3823i | 1.05076 | − | 1.05076i | ||||
\(893\) | 2.15957 | − | 2.15957i | 0.0722674 | − | 0.0722674i | ||||
\(894\) | 0.232110 | − | 0.0961433i | 0.00776293 | − | 0.00321551i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.68527 | + | 1.11228i | 0.0897087 | + | 0.0371586i | ||||
\(897\) | 0.723619 | 0.0241609 | ||||||||
\(898\) | −8.18648 | − | 3.39095i | −0.273186 | − | 0.113157i | ||||
\(899\) | −10.1131 | + | 10.1131i | −0.337290 | + | 0.337290i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.78332 | + | 5.18106i | 0.325930 | + | 0.172606i | ||||
\(902\) | − | 3.10018i | − | 0.103225i | ||||||
\(903\) | 0.0937705 | + | 0.0937705i | 0.00312049 | + | 0.00312049i | ||||
\(904\) | −5.87267 | + | 14.1779i | −0.195322 | + | 0.471549i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.345949 | + | 0.143297i | 0.0114934 | + | 0.00476072i | ||||
\(907\) | −5.55499 | + | 2.30095i | −0.184450 | + | 0.0764018i | −0.472997 | − | 0.881064i | \(-0.656828\pi\) |
0.288547 | + | 0.957466i | \(0.406828\pi\) | |||||||
\(908\) | −14.7147 | − | 35.5244i | −0.488324 | − | 1.17892i | ||||
\(909\) | 14.6679 | + | 14.6679i | 0.486505 | + | 0.486505i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.5802 | + | 13.9094i | −1.11256 | + | 0.460839i | −0.861820 | − | 0.507215i | \(-0.830675\pi\) |
−0.250744 | + | 0.968054i | \(0.580675\pi\) | |||||||
\(912\) | −0.457403 | + | 0.189462i | −0.0151461 | + | 0.00627373i | ||||
\(913\) | −16.4936 | + | 39.8190i | −0.545858 | + | 1.31782i | ||||
\(914\) | − | 2.74173i | − | 0.0906883i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −35.1724 | + | 35.1724i | −1.16213 | + | 1.16213i | ||||
\(917\) | − | 5.17440i | − | 0.170874i | ||||||
\(918\) | −0.0455080 | + | 0.480989i | −0.00150199 | + | 0.0158750i | ||||
\(919\) | −31.4827 | −1.03852 | −0.519259 | − | 0.854617i | \(-0.673792\pi\) | ||||
−0.519259 | + | 0.854617i | \(0.673792\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.114956 | − | 0.277529i | 0.00378794 | − | 0.00914489i | ||||
\(922\) | 2.60127 | 0.0856684 | ||||||||
\(923\) | −4.46025 | + | 10.7680i | −0.146811 | + | 0.354433i | ||||
\(924\) | 0.0320884 | + | 0.0774682i | 0.00105563 | + | 0.00254852i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.86821 | − | 5.86821i | −0.192841 | − | 0.192841i | ||||
\(927\) | 27.4742 | − | 27.4742i | 0.902371 | − | 0.902371i | ||||
\(928\) | 7.15312 | + | 17.2692i | 0.234813 | + | 0.566888i | ||||
\(929\) | 16.5321 | + | 39.9121i | 0.542402 | + | 1.30947i | 0.923024 | + | 0.384743i | \(0.125710\pi\) |
−0.380622 | + | 0.924731i | \(0.624290\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 19.4812i | − | 0.638471i | ||||||
\(932\) | −40.6032 | − | 16.8184i | −1.33000 | − | 0.550905i | ||||
\(933\) | −0.865552 | − | 0.865552i | −0.0283369 | − | 0.0283369i | ||||
\(934\) | −10.7732 | −0.352511 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.27195 | −0.270377 | ||||||||
\(937\) | −8.15745 | − | 8.15745i | −0.266492 | − | 0.266492i | 0.561193 | − | 0.827685i | \(-0.310343\pi\) |
−0.827685 | + | 0.561193i | \(0.810343\pi\) | |||||||
\(938\) | 1.24860 | + | 0.517188i | 0.0407683 | + | 0.0168868i | ||||
\(939\) | − | 0.660917i | − | 0.0215682i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.4367 | − | 25.1965i | −0.340227 | − | 0.821382i | −0.997692 | − | 0.0678965i | \(-0.978371\pi\) |
0.657465 | − | 0.753485i | \(-0.271629\pi\) | |||||||
\(942\) | 0.0202054 | + | 0.0487801i | 0.000658327 | + | 0.00158934i | ||||
\(943\) | 14.8201 | − | 14.8201i | 0.482608 | − | 0.482608i | ||||
\(944\) | −20.9608 | − | 20.9608i | −0.682217 | − | 0.682217i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.12268 | + | 7.53882i | 0.101527 | + | 0.245108i | ||||
\(947\) | −8.72231 | + | 21.0575i | −0.283437 | + | 0.684278i | −0.999911 | − | 0.0133362i | \(-0.995755\pi\) |
0.716474 | + | 0.697614i | \(0.245755\pi\) | |||||||
\(948\) | 1.08085 | 0.0351045 | ||||||||
\(949\) | 0.164134 | − | 0.396254i | 0.00532801 | − | 0.0128630i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.19198 | −0.0386527 | ||||||||
\(952\) | 1.70960 | + | 0.161752i | 0.0554086 | + | 0.00524240i | ||||
\(953\) | − | 28.9548i | − | 0.937938i | −0.883215 | − | 0.468969i | \(-0.844626\pi\) | ||
0.883215 | − | 0.468969i | \(-0.155374\pi\) | |||||||
\(954\) | −2.04990 | + | 2.04990i | −0.0663681 | + | 0.0663681i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.83243i | 0.318003i | ||||||||
\(957\) | −0.271453 | + | 0.655346i | −0.00877483 | + | 0.0211843i | ||||
\(958\) | −3.21425 | + | 1.33139i | −0.103848 | + | 0.0430152i | ||||
\(959\) | 3.85667 | − | 1.59748i | 0.124538 | − | 0.0515854i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4447 | + | 15.4447i | 0.498216 | + | 0.498216i | ||||
\(962\) | 2.57115 | + | 6.20731i | 0.0828972 | + | 0.200132i | ||||
\(963\) | 10.0335 | − | 4.15603i | 0.323326 | − | 0.133926i | ||||
\(964\) | −9.39800 | − | 3.89278i | −0.302689 | − | 0.125378i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.0150540 | − | 0.0363436i | 0.000484355 | − | 0.00116934i | ||||
\(967\) | −35.7870 | − | 35.7870i | −1.15083 | − | 1.15083i | −0.986386 | − | 0.164447i | \(-0.947416\pi\) |
−0.164447 | − | 0.986386i | \(-0.552584\pi\) | |||||||
\(968\) | − | 4.65968i | − | 0.149768i | ||||||
\(969\) | −0.485761 | + | 0.401787i | −0.0156049 | + | 0.0129073i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.2222 | − | 23.2222i | 0.745236 | − | 0.745236i | −0.228344 | − | 0.973580i | \(-0.573331\pi\) |
0.973580 | + | 0.228344i | \(0.0733312\pi\) | |||||||
\(972\) | 2.52697 | + | 1.04671i | 0.0810527 | + | 0.0335731i | ||||
\(973\) | −1.08154 | −0.0346727 | ||||||||
\(974\) | −1.60761 | − | 0.665895i | −0.0515112 | − | 0.0213366i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −33.4883 | + | 13.8713i | −1.07193 | + | 0.444010i | ||||
\(977\) | −15.2966 | + | 15.2966i | −0.489381 | + | 0.489381i | −0.908111 | − | 0.418730i | \(-0.862475\pi\) |
0.418730 | + | 0.908111i | \(0.362475\pi\) | |||||||
\(978\) | 0.236338 | − | 0.236338i | 0.00755727 | − | 0.00755727i | ||||
\(979\) | 3.96956 | − | 1.64425i | 0.126868 | − | 0.0525503i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.2610 | − | 5.90708i | −0.455317 | − | 0.188599i | ||||
\(982\) | 7.73637 | 0.246878 | ||||||||
\(983\) | 4.72148 | + | 1.95570i | 0.150592 | + | 0.0623771i | 0.456706 | − | 0.889618i | \(-0.349029\pi\) |
−0.306115 | + | 0.951995i | \(0.599029\pi\) | |||||||
\(984\) | 0.166283 | − | 0.166283i | 0.00530092 | − | 0.00530092i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.47423 | + | 5.40935i | 0.142489 | + | 0.172269i | ||||
\(987\) | − | 0.0175531i | − | 0.000558720i | ||||||
\(988\) | −7.37963 | − | 7.37963i | −0.234777 | − | 0.234777i | ||||
\(989\) | −21.1108 | + | 50.9661i | −0.671286 | + | 1.62063i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.32187 | + | 0.961750i | 0.0737566 | + | 0.0305510i | 0.419257 | − | 0.907868i | \(-0.362291\pi\) |
−0.345500 | + | 0.938419i | \(0.612291\pi\) | |||||||
\(992\) | −11.0578 | + | 4.58029i | −0.351085 | + | 0.145424i | ||||
\(993\) | 0.300170 | + | 0.724673i | 0.00952559 | + | 0.0229968i | ||||
\(994\) | 0.448030 | + | 0.448030i | 0.0142107 | + | 0.0142107i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.45957 | + | 0.604572i | −0.0462481 | + | 0.0191566i | ||||
\(997\) | 33.3033 | − | 13.7947i | 1.05473 | − | 0.436882i | 0.213149 | − | 0.977020i | \(-0.431628\pi\) |
0.841576 | + | 0.540138i | \(0.181628\pi\) | |||||||
\(998\) | −2.56951 | + | 6.20336i | −0.0813366 | + | 0.196364i | ||||
\(999\) | − | 3.06441i | − | 0.0969535i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 425.2.n.c.399.4 | 24 | ||
5.2 | odd | 4 | 85.2.l.a.76.3 | yes | 24 | ||
5.3 | odd | 4 | 425.2.m.b.76.4 | 24 | |||
5.4 | even | 2 | 425.2.n.f.399.3 | 24 | |||
15.2 | even | 4 | 765.2.be.b.586.4 | 24 | |||
17.15 | even | 8 | 425.2.n.f.49.3 | 24 | |||
85.7 | even | 16 | 1445.2.a.q.1.8 | 12 | |||
85.27 | even | 16 | 1445.2.a.p.1.8 | 12 | |||
85.32 | odd | 8 | 85.2.l.a.66.3 | ✓ | 24 | ||
85.49 | even | 8 | inner | 425.2.n.c.49.4 | 24 | ||
85.57 | even | 16 | 1445.2.d.j.866.9 | 24 | |||
85.58 | even | 16 | 7225.2.a.bq.1.5 | 12 | |||
85.62 | even | 16 | 1445.2.d.j.866.10 | 24 | |||
85.78 | even | 16 | 7225.2.a.bs.1.5 | 12 | |||
85.83 | odd | 8 | 425.2.m.b.151.4 | 24 | |||
255.32 | even | 8 | 765.2.be.b.406.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
85.2.l.a.66.3 | ✓ | 24 | 85.32 | odd | 8 | ||
85.2.l.a.76.3 | yes | 24 | 5.2 | odd | 4 | ||
425.2.m.b.76.4 | 24 | 5.3 | odd | 4 | |||
425.2.m.b.151.4 | 24 | 85.83 | odd | 8 | |||
425.2.n.c.49.4 | 24 | 85.49 | even | 8 | inner | ||
425.2.n.c.399.4 | 24 | 1.1 | even | 1 | trivial | ||
425.2.n.f.49.3 | 24 | 17.15 | even | 8 | |||
425.2.n.f.399.3 | 24 | 5.4 | even | 2 | |||
765.2.be.b.406.4 | 24 | 255.32 | even | 8 | |||
765.2.be.b.586.4 | 24 | 15.2 | even | 4 | |||
1445.2.a.p.1.8 | 12 | 85.27 | even | 16 | |||
1445.2.a.q.1.8 | 12 | 85.7 | even | 16 | |||
1445.2.d.j.866.9 | 24 | 85.57 | even | 16 | |||
1445.2.d.j.866.10 | 24 | 85.62 | even | 16 | |||
7225.2.a.bq.1.5 | 12 | 85.58 | even | 16 | |||
7225.2.a.bs.1.5 | 12 | 85.78 | even | 16 |